Answer :

Answer:

Nick = 13 years old.

Step-by-step explanation:

Define the variables:

  • Let n = the age of Nick (in years).
  • Let w = the age of Will (in years).

Given:

  • Nick is 5 years older than Will.
  • The sum of their ages is 21.

Create a system of equations with the given information and defined variables:

[tex]\begin{cases} w=n-5\\n+w=21\end{cases}[/tex]

Substitute the first equation into the second equation and solve for n:

[tex]\implies n+(n-5)=21[/tex]

[tex]\implies 2n-5=21[/tex]

[tex]\implies 2n-5+5=21+5[/tex]

[tex]\implies 2n=26[/tex]

[tex]\implies 2n \div 2=26 \div 2[/tex]

[tex]\implies n=13[/tex]

Therefore, Nick is 13 years old.

To find the age of Will, simply substitute the found value of n into the first equation and solve for w:

[tex]\implies w=13-5[/tex]

[tex]\implies w=8[/tex]

Therefore, Will is 8 years old.